Arithmetic sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Arithmetic sequences.

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ID	Problem	Count
7651	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 40000 ~~ \text{and} ~~ d = 1600 $.	1
7652	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	1
7653	Find $ S_{ 59500 } $ ( sum of first $ 59500 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $.	1
7654	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $.	1
7655	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = 1 $.	1
7656	Find $ S_{ 76 } $ ( sum of first $ 76 $ terms ) of arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = 1 $.	1
7657	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 9 $.	1
7658	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 2 $.	1
7659	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 7 $.	1
7660	Find $ S_{ 91 } $ ( sum of first $ 91 $ terms ) of arithmetic progression if $ a_1 = 51 ~~ \text{and} ~~ d = 1 $.	1
7661	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	1
7662	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 1 $.	1
7663	$$ a_1 = -1 ~,~ d = \frac{ 1 }{ 2 } ~,~ a_n = 1 ~,~ n = ? $$	1
7664	Find $ S_{ 194 } $ ( sum of first $ 194 $ terms ) of arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = 50 $.	1
7665	Find $ a_1 $ (first term of arithmetic progression) if $ d = 7 ~~ \text{and} ~~ S_{ 37 } = 5032 $.	1
7666	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 7 $.	1
7667	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 25 $.	1
7668	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 133 ~~ \text{and} ~~ d = 78 $.	1
7669	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 12 $.	1
7670	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 334 ~~ \text{and} ~~ d = -1 $.	1
7671	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 160 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	1
7672	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	1
7673	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 119 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	1
7674	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 118 ~~ \text{and} ~~ d = 7 $.	1
7675	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 116 ~~ \text{and} ~~ d = 7 $.	1
7676	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 115 ~~ \text{and} ~~ d = 7 $.	1
7677	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 114 ~~ \text{and} ~~ d = 7 $.	1
7678	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 113 ~~ \text{and} ~~ d = 7 $.	1
7679	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 113 ~~ \text{and} ~~ d = 7 $.	1
7680	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 112 ~~ \text{and} ~~ d = 7 $.	1
7681	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 144 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	1
7682	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 114 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	1
7683	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 116 ~~ \text{and} ~~ d = \frac{ 56 }{ 9 } $.	1
7684	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	1
7685	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
7686	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = -3 $.	1
7687	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = -3 $.	1
7688	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
7689	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = -3 $.	1
7690	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	1
7691	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	1
7692	Find $ a_1 $ (first term of arithmetic progression) if $ d = -2 ~~ \text{and} ~~ a_{ 21 } = 65 $.	1
7693	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 4 $.	1
7694	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
7695	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = -1 $.	1
7696	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 75 ~~ \text{and} ~~ d = 5 $.	1
7697	Find $ a_{ 120 } $ of an arithmetic progression if $ a_1 = 75 ~~ \text{and} ~~ d = 5 $.	1
7698	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 75 ~~ \text{and} ~~ d = 5 $.	1
7699	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 75 ~~ \text{and} ~~ d = 5 $.	1
7700	Find $ S_{ 80 } $ ( sum of first $ 80 $ terms ) of arithmetic progression if $ a_1 = 75 ~~ \text{and} ~~ d = 5 $.	1